Rank Preserving Code-based Signature

Abstract

We propose a rank metric code-based signature scheme constructed via the Schnorr approach. We define a new problem in rank metric coding theory, namely the Rank Vector Decomposition problem and analyze its solving complexity. The hardness of our signature scheme is based on the Rank Syndrome Decoding problem, Rank Support Basis Decomposition problem and Rank Vector Decomposition problem. We also give detailed analysis for the structural security of our signature scheme. Then, we provide parameters for our constructed signature scheme and compare our scheme with other existing secure rank metric signature schemes. Our signature scheme requires only public key size of 443 bytes and signature size of 4.03 kilobytes for 128-bit security level.